Question

Suppose the dollars per pound spot rate is $1.31/£ and the 12-month forward rate implies a forward discount of 4.00% on the pound. What must be the 12-month forward rate? [hint: The pound is traded at a discount in the forward market, compared to spot trades]

Suppose the three-month forward rate for the Indian rupees (INR) per Japanese yen (JPY) was INR 0.75/JPY, while the spot rate at the time was INR 0.73/JPY. A scientist located in New York speculates that the spot rate three months later will be INR 0.77/JPY. They decided to devote 500,000 yen in order to try to profit from this speculation, by making a trade in the forward market. Describe the cash flows and the profit if the prediction comes true (Specify the amounts and currencies). [hint: the trade was made in the forward market; it was not a buy-and-hold strategy of ¥ nor ₹]

An option trader purchased a call option on Russian ruble (₽) with a strike price of $0.01350/₽, at a premium of 0.00040 dollars per ruble and with an expiration date three months from now. The option is for ₽2,500,000. (a) What would be the trader’s profit or loss if the spot rate at maturity is $0.01310/₽? (b) What would be the trader’s profit or loss if the spot rate at maturity is $0.01380/₽?

Answer 1

In the question the given spot exchange rate is $1.31/£ and 12 month forward rate implies forward discount of 4% on pound.

Now we know,

When annualised percentage is positive, then the currency which is taken as 1 unit is at a forward premium and other is at a forward discount and vice versa.

Here it is given that forward discount is on pound, and pound in the spot exchange rate is given in 1unit. Therefore the annualised percentage is in negative.

Now we know,

Annualised Forward Discount

= {(Mid Value of Forward Rate - Mid Value of Spot Rate) / Mid Value of Spot Rate} * (12/n) * 100

where n = number of months which is 12 in this case.

As we are provided with single spot rate, ( that is ask rate and bid rate are not seperately given) we will consider that as "Mid Spot Rate." i.e. Mid Spot Rate = $1.31/£.

Let Mid Forward Rate be a single rate and let it be $ X/£.

Therefore putting values to the above formula we get,

-4 = {(X-1.31)/1.31} *(12/12)*100

or, -4 = {(100X - 131) / 1.31}

or,(-4) * 1.31 = 100X - 131

or, -5.24 + 131 = 100X

or,125.76 = 100X

or, X = 125.76/ 100

or, X = 1.2576.

Therefore the 12 month forward rate is $1.2576/£.